Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Analysis of the inflection points of height-diameter models

The inflection point is an important feature of sigmoidal height-diameter(H-D)models.It is often cited as one of the properties favoring sigmoidal model forms.However,there are very few studies analyzing the inflection points of H-D models.The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset.The six models were the Wykoff(WYK),Schumacher(SCH),Curtis(CUR),HossfeldⅣ(HOS),von Bertalanffy-Richards(VBR),and Gompertz(GPZ)models.The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution.The distributions of the estimated inflection points were similar between the two-parameter models WYK,SCH,and CUR,but were different between the threeparameter models HOS,VBR,and GPZ.GPZ produced some of the largest inflection points.HOS and VBR produced concave H-D curves without inflection points for 12.7%and 39.7%of the tree species.Evergreen species or decreasing shade tolerance resulted in larger inflection points.The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape.Furthermore,HOS could produce concave H-D curves for portions of the landscape.Based on the studied behaviors,the choice between two-parameter models may not matter.We recommend comparing seve ral three-parameter model forms for consistency in estimated inflection points before deciding on one.Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one.Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.

Blood-letting punctures at twelve Jing-Well points of the hand can treat cerebral ischemia in a similar manner to mannitol

A rat model of middle cerebral artery permanent occlusion was established using the modified Longa method. Successfully established model animals were treated by blood-letting puncture at twelve Jing-Well points of the hand, and/or by injecting mannitol into the caudal vein twice daily. Brain tissue was collected at 24, 48 and 72 hours after modeling, and blood was collected through the retinal vein before Evans blue was injected, approximately 1 hour prior to harvesting of brain tissue. Results showed that Evans blue leakage into brain tissue and serum nitric oxide synthase activity were significantly increased in model rats. Treatment with blood-letting punctures at twelve Jing-Well points of the hand and/or injection of mannitol into the caudal vein reduced the amount of Evans blue leakage into the brain tissue and serum nitric oxide synthase activity to varying degrees. There was no significant difference between single treatment and combined treatment. Experimental findings indicate that blood-letting punctures at twelve Jing-Well points of the hand can decrease blood-brain barrier permeability and serum nitric oxide synthase activity in rats following middle cerebral artery occlusion, and its effect is similar to that of mannitol injection alone and Jing-Well points plus mannitol injection.

Treatment of Migraine with Acupuncture at Points Pertaining to the Liver and Gallbladder Channels

In studying the syndrome of yang-hyperactivity, we found that most migraine patients were with hyperactivity of the liver-yang, stagnation of the liver-qiand blood stasis, and stagnation of the liverqi and deficiency of the spleen. To evaluate the needling effects on migraine and to approach its mechanism, we have launched a study in 207 cases since 1997. The results were satisfactory and reported as follows.

Semantic model and optimization of creative processes at mathematical knowledge formation

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

Analysis of the Significance of Key Points of Patient Interventional Psychological Care and Pain Care

Interventional therapy has become increasingly popular in clinical practice due to advancements in medical technology.However,patients often experience psychological and physiological pressure due to its invasive nature.The management of patient discomfort and tension is crucial to ensure effective treatment.Psychological and pain management are essential components of interventional therapy,as they significantly impact patient recovery and prognosis.This article discussed the importance of interventional psychological and pain care for patients,starting with the development and spread of interventional therapy.The significance of providing high-quality nursing services to patients and improving their quality of life was also discussed.

Cyberattack Ramifications, The Hidden Cost of a Security Breach

In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term consequences that businesses encounter. This study integrates findings from various research, including quantitative reports, drawing upon real-world incidents faced by both small and large enterprises. This investigation emphasizes the profound intangible costs, such as trade name devaluation and potential damage to brand reputation, which can persist long after the breach. By collating insights from industry experts and a myriad of research, the study provides a comprehensive perspective on the profound, multi-dimensional impacts of cybersecurity incidents. The overarching aim is to underscore the often-underestimated scope and depth of these breaches, emphasizing the entire timeline post-incident and the urgent need for fortified preventative and reactive measures in the digital domain.

Spatial Pattern and Influencing Factor Analysis of Attended Collection and Delivery Points in Changsha City, China

Attended collection and delivery points are vital components of ‘last-mile logistics’.Based on point of interest(POI) data for Cainiao Stations and China Post stations in Changsha City, China, this paper provides a detailed exploration of the basic features, spatial distribution, and location influencing factors of attended collection and delivery points.Specifically, analyses of the types, service objects and location distributions of the attended collection and delivery points alongside a discussion of their spatial pattern and influencing factors provides a reference for their general geographic layout and characteristics.The findings of this study indicate that: 1) The main mode of operation of attended collection and delivery points is franchises, with other modes of operation rely on supermarkets and other individual shop types.2) The main service targets of attended collection and delivery points are communities, schools, and businesses, followed by townships, enterprises, scenic spots, and administrative units.3) Approximately 77.44% of the attended collection and delivery points are located near the exits of service areas;others are situated in the centre of the service areas.For the Cainiao Stations, 80% are located within 125 m of the exit;for the China Post stations, 80% are located within 175 m of the exit.4) The spatial distribution of the attended collection and delivery points in Changsha is unbalanced, with ‘more centre and fewer surrounding’.The centre is an ‘inverted triangle’, and the edge is an ‘orphan’, showing a northwest-southeast orientation and symmetrical along the axis.The layout of the attended collection and delivery points forms three core areas, and the number of sites decreases with the distance from the core.5) The number and distribution of the attended collection and delivery points are strongly consistent with the regional economic development level, population, and roadway system traffic convenience.Most attended collection and delivery points are on residential, scientific and educational, and commercial and financial land.

GRAPHICAL COMPUTING METHOD ON FOUR-BAR LINKAGE(1)——Inflexion Circle,Focal Axis,Ball's Point,Centering-point Curve and Circling-point Curve For Four ISPs,Coupler Curves Based on Ball's Points——

By means of programs GTMPAC based- on generalized triangle method,analysis and synthesis of mechanism design in accordance with absolutely graphicalmethod( absolutely germetrical method) are developed.In this paper,we make aspecial study about centering- point curve and circling- point curve and couplercurves based on Ball’s points.

Prediction of collapse process and tipping points for mutualistic and competitive networks with k-core method

Ecosystems generally have the self-adapting ability to resist various external pressures or disturbances,which is always called resilience.However,once the external disturbances exceed the tipping points of the system resilience,the consequences would be catastrophic,and eventually lead the ecosystem to complete collapse.We capture the collapse process of ecosystems represented by plant-pollinator networks with the k-core nested structural method,and find that a sufficiently weak interaction strength or a sufficiently large competition weight can cause the structure of the ecosystem to collapse from its smallest k-core towards its largest k-core.Then we give the tipping points of structure and dynamic collapse of the entire system from the one-dimensional dynamic function of the ecosystem.Our work provides an intuitive and precise description of the dynamic process of ecosystem collapse under multiple interactions,and provides theoretical insights into further avoiding the occurrence of ecosystem collapse.

Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

BIFURCATION OF SINGULAR POINTS NEAR A DOUBLE FOLD POINT INZ_2 -SYMMETRIC NONLINEAR EQUATIONS

We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.

Simple Singular Perturbation Problems with Turning Points

The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.

THE APPLICATION OF THE ELECTRIC INFORMATION MEASURE ON HUMAN AURICULAR POINTS TO THE UPPER-DIGESTIVE-TRACT CANCER SURVEY

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The Evil of ‘Reciting’

First of all it is necessary to point out that 'reciting' is the wrong term for what Chinese students are often asked to do when they are learning English. The correct terms are, 'learning by heart' or 'rote learning'. In this article the term 'rote learning' will be used.……

End points of clinical trials in metastatic castration-resistant prostate cancer:A systematic review

AIM： To review the defnition and performance of the commonly used end points in trials of systemic thera-pies in metastatic castration-resistant prostate cancer patients. METHODS： A literature search was undertaken on PubMed database to identify studies meeting estab-lished criteria, with the aim of selecting randomized clinical trials and study definition and performance of their end points. The end points were grouped into three categories： overall survival （OS）, time-to-event end points, and response end points. A special analysis was performed for secondary end points of the studies which documented a beneft in OS in the experimental arm. Finally, publishes analyses for surrogacy of the in-cluded end points were also reported. RESULTS： OS, time-to-event and response end points in 31 selected trials were analyzed. OS was the pri-mary end point in 14 trials, and the secondary end point in 17. A time-to-event end point was the primaryend point in 8 studies, and the secondary end point in 22; the most reported time-to-event end points were composite end points, and the events changed among trials. A response end point was the primary end point in 9 studies, in 3 it was prostate-specifc antigen （PSA）-related, in 3 pain-related and in 3 mixed. A response end point was the secondary end point in 19 studies： PSA response and radiologic response were the most frequently used secondary end points in 19 and 11 tri-als, respectively, while pain response was used in 5 studies.CONCLUSION： A homogeneous defnition of progres-sion in future trials is mandatory. Among response end points, pain-response and PSA-response appear to be the most reliable.

Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid

The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.

An Interpretation of Points of View in A Thousand Splendid Suns

As the second bestseller of Khaled Hosseini' s novels that spread all over the world,A Thousand Splendid Suns embodies the quite impressive and infective writing techniques and narrative power of its writer and it also shows the unique language style of Hosseini.This paper gives an explanation of the narrative point of view and analyses the specific examples in the text.Through deepening the transition of third-person point of view between the two characters,the paper demonstrates its stylistic effects in arranging the textual structure as well as building the characters,thus deepen the theme of the whole story.

The Bezier Control Points Method for Solving Delay Differential Equation

In this paper, Bezier surface form is used to find the approximate solution of delay differential equations (DDE’s). By using a recurrence relation and the traditional least square minimization method, the best control points of residual function can be found where those control points determine the approximate solution of DDE. Some examples are given to show efficiency of the proposed method.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.